Finite Group Databasebeta

← #7672360

Subgroups — #7672360

Order 512.

4980 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59665C212yesmaximal, complemented
2#59639C212yesmaximal, complemented
3#59456C212yesmaximal, complemented
4#59426C212yesmaximal, complemented
5#59289C214yesmaximal, complemented
6#59111C214yesmaximal, complemented
7#39535C214yesmaximal, complemented
8#39534C214yesmaximal, complemented
9#39192C212yesmaximal, complemented
10#38976C212yesmaximal, complemented
11#38111C214yesmaximal, complemented
12#36645C211yesmaximal, characteristic, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36563C211yesmaximal, characteristic, complemented
15#36194C211yesmaximal, characteristic, complemented
16#36193C212yesmaximal, complemented
17#36186C212yesmaximal
18#36181C212yesmaximal, complemented
19#36177C212yesmaximal, complemented
20#36176C212yesmaximal
21#36134C211yesmaximal, characteristic, complemented
22#36129C212yesmaximal, complemented
23#35594C214yesmaximal, complemented
24#35291C212yesmaximal, complemented
25#35247C212yesmaximal
26#34225C212yesmaximal, complemented
27#34196C212yesmaximal, complemented
28C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
29C4×#529C211yesmaximal, characteristic
30C2×#552C2214yes—
31C2×#533C2212yes—
32C2×#533C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2211yescharacteristic
35C22×C4×Q8C2212yes—
36#2868C2211yescharacteristic
37#2868C2211yescharacteristic
38#2862C2212yes—
39#2862C2212yes—
40#2859C2212yes—
41#2859C2212yes—
42#2859C2212yes—
43#2857C2212yes—
44#2857C2212yes—
45#2857C2212yes—
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2855C2214yes—
50#2854C2214yes—
51#2799C2218yes—
52#2798C2218yes—
53#2772C2218yes—
54#2766C2218yes—
55#2759C2218yes—
56#2755C2218yes—
57#2725C2218yes—
58#2719C2218yes—
59#2645C2214yes—
60#2637C2218yes—
61#2625C2214yes—
62#2596C2218yes—
63#2592C2214yes—
64#2585C2218yes—
65#2584C2214yes—
66#2582C2212yes—
67#2582C2212yes—
68#2571C2212yes—
69#2571C2212yes—
70#2570C2214yes—
71#2568C2212yes—
72#2567C2212yes—
73#2565C2214yes—
74#2563C2212yes—
75#2552C2212yes—
76#2552C2212yes—
77#2550C2214yes—
78#2550C2214yes—
79#2542C2212yes—
80#2538C2212yes—
81#2538C2212yes—
82#2533C2218yes—
83#2532C2218yes—
84#2520C2218yes—
85#2519C2218yes—
86#2514C2214yes—
87#2514C2214yes—
88#2513C2214yes—
89#2512C2214yes—
90#2511C2214yes—
91#2511C2214yes—
92#2509C2214yes—
93#2509C2214yes—
94#2508C2214yes—
95#2508C2214yes—
96#2507C2214yes—
97#2507C2214yes—
98#2506C2214yes—
99#2506C2214yes—
100#2506C2214yes—
101#2503C2214yes—
102#2499C2214yes—
103#2498C2218yes—
104#2497C2214yes—
105#2496C2214yes—
106#2496C2214yes—
107#2495C2214yes—
108#2494C2214yes—
109#2493C2218yes—
110#2492C2214yes—
111#2492C2214yes—
112#2489C2214yes—
113#2488C2218yes—
114#2486C2214yes—
115#2486C2214yes—
116#2469C2218yes—
117#2453C2218yes—
118#2453C2214yes—
119#2451C2214yes—
120#2451C2214yes—
121#2446C2214yes—
122#2446C2214yes—
123#2442C2214yes—
124#2441C2214yes—
125#2439C2214yes—
126#2439C2214yes—
127#2438C2218yes—
128#2429C2214yes—
129#2429C2214yes—
130#2423C2214yes—
131#2421C2214yes—
132#2417C2214yes—
133#2413C2218yes—
134#2409C2214yes—
135#2370C2214yes—
136#2370C2214yes—
137#2369C2212yes—
138#2369C2212yes—
139#2365C2212yes—
140#2365C2212yes—
141#2362C2214yes—
142#2362C2214yes—
143#2360C2214yes—
144#2356C2214yes—
145#2355C2214yes—
146#2355C2212yes—
147#2355C2214yes—
148#2355C2212yes—
149#2355C2212yes—
150#2355C2212yes—
151#2354C2212yes—
152#2354C2212yes—
153#2352C2214yes—
154#2351C2214yes—
155Q8×C4⋊C4C2212yes—
156Q8×C4⋊C4C2212yes—
157#2347C2214yes—
158#2346C2214yes—
159#2344C2214yes—
160#2344C2214yes—
161#2344C2218yes—
162Q8×C22⋊C4C2214yes—
163#2323C2214yes—
164#2323C2214yes—
165#2323C2214yes—
166#2320C2214yes—
167#2320C2214yes—
168#2320C2218yes—
169C4×C4⋊Q8C2212yes—
170C4×C4⋊Q8C2212yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×#125C2211yescharacteristic
186C4×#125C2211yescharacteristic
187C4×#126C2212yes—
188C4×#126C2212yes—
189C4×#124C2211yescharacteristic
190C4×#124C2211yescharacteristic
191C4×C22⋊Q8C2211yescharacteristic
192C4×C22⋊Q8C2211yescharacteristic
193C4×#123C2212yes—
194C4×#123C2212yes—
195C4×#121C2211yescharacteristic
196C4×#121C2211yescharacteristic
197#2298C2212yes—
198#2295C2211yescharacteristic
199C2×#391C2212yes—
200#2293C2211yescharacteristic
201C2×#389C2212yes—
202C2×#389C2212yes—
203#2290C2212yes—
204#2285C2212yes—
205#2285C2212yes—
206#2285C2212yes—
207#2285C2214yes—
208C2×#384C2211yescharacteristic
209#2283C2214yes—
210#2283C2211yescharacteristic
211#2276C2214yes—
212C42×Q8C2211yescharacteristic
213C42×D4C2212yes—
214C42×D4C2211yescharacteristic
215C4×#117C2212yes—
216C2×C4×C4⋊C4C2212yes—
217C2×C4×C4⋊C4C2212yes—
218C2×C43C2211yescharacteristic
219C23×Q8C2312yes—
220#552—416no—
221#533—216no—
222#533—48no—
223C2×C4⋊Q8—28no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2312yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2312yes—
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235#529—28no—
236C2×#126C2312yes—
237C2×#126C2318yes—
238C2×#125C2311yescharacteristic
239C2×#125C2314yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#125C2318yes—
243C2×#124C2311yescharacteristic
244C2×#123C2312yes—
245C2×#123C2318yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×#121C2311yescharacteristic
254C2×C4×Q8—216no—
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2312yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2314yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2314yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2314yes—
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2312yes—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2312yes—
276C2×#117C2312yes—
277C2×#117C2314yes—
278C2×#117C2312yes—
279C2×#117C2318yes—
280C2×#117C2314yes—
281C2×#117C2314yes—
282C22×C4⋊C4C2314yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C42C2314yes—
289C22×C42C2311yescharacteristic
290C22×C42C2312yes—
291C22×C42C2311yescharacteristic
292C22×C42C2311yescharacteristic
293C22×C42C2311yescharacteristic
294C22×C42C2311yescharacteristic
295C22×C42C2311yescharacteristic
296C22×C42C2311yescharacteristic
297#401C2318yes—
298#400C2318yes—
299#400C2318yes—
300#400C2318yes—
301#400C2318yes—
302#400C2318yes—
303#400C2318yes—
304#400C2318yes—
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#399C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#398C2318yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2318yes—
321#397C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#395C2318yes—
326#395C2318yes—
327#393C2318yes—
328#393C2318yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2314yes—
346#391C2314yes—
347#391C2318yes—
348#391C2318yes—
349#391C2314yes—
350#391C2314yes—
351#391C2318yes—
352#391C2318yes—
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390C2314yes—
356#390C2314yes—
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2318yes—
394#389C2318yes—
395#389C2314yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2318yes—
405#388C2312yes—
406#388C2312yes—
407#388C2312yes—
408#388C2312yes—
409#388C2312yes—
410#388C2312yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2312yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2312yes—
422#387C2312yes—
423#387C2312yes—
424#387C2312yes—
425#387C2312yes—
426#387C2312yes—
427#387C2312yes—
428#387C2312yes—
429#387C2312yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#386C2318yes—
450#386C2312yes—
451#386C2312yes—
452#385C2318yes—
453#385C2312yes—
454#385C2312yes—
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2311yescharacteristic
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2314yes—
465#384C2312yes—
466#384C2312yes—
467#384C2312yes—
468#384C2312yes—
469#384C2314yes—
470#383C2312yes—
471#383C2318yes—
472#383C2318yes—
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2314yes—
476#382C2314yes—
477#382C2314yes—
478#382C2314yes—
479#382C2314yes—
480#382C2314yes—
481#382C2318yes—
482#382C2318yes—
483#382C2314yes—
484#382C2314yes—
485#381C2318yes—
486#381C2312yes—
487#381C2318yes—
488#380C2314yes—
489#380C2314yes—
490#380C2314yes—
491#380C2314yes—
492#380C2314yes—
493#380C2318yes—
494#380C2314yes—
495#380C2314yes—
496#380C2314yes—
497#380C2314yes—
498#380C2314yes—
499#380C2311yescharacteristic
500#380C2311yescharacteristic
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2312yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2312yes—
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2312yes—
522C4×C4⋊C4C2312yes—
523C4×C4⋊C4C2312yes—
524C4×C4⋊C4C2312yes—
525C4×C4⋊C4C2314yes—
526C4×C4⋊C4C2314yes—
527C4×C4⋊C4C2314yes—
528C4×C4⋊C4C2314yes—
529C4×C4⋊C4C2314yes—
530C4×C4⋊C4C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2318yes—
535C4×C4⋊C4C2318yes—
536C4×C4⋊C4C2318yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2311yescharacteristic
539C4×C4⋊C4C2311yescharacteristic
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2312yes—
545C4×C4⋊C4C2312yes—
546C4×C22⋊C4C2312yes—
547C4×C22⋊C4C2312yes—
548C4×C22⋊C4C2312yes—
549C4×C22⋊C4C2312yes—
550C4×C22⋊C4C2312yes—
551C4×C22⋊C4C2312yes—
552C4×C22⋊C4C2312yes—
553C4×C22⋊C4C2318yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560#376C2312yes—
561#376C2312yes—
562#376C2318yes—
563C2×#95C2314yes—
564C2×#95C2314yes—
565C43C2311yescharacteristic
566C43C2311yescharacteristic
567C43C2311yescharacteristic
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2312yes—
573C43C2311yescharacteristic
574C22×Q8—28no—
575C22×Q8—28no—
576C22×Q8—44no—
577C22×Q8C2414yes—
578C22×Q8C2411yescharacteristic
579C22×Q8C2412yes—
580C22×Q8C2414yes—
581C22×Q8C2412yes—
582C22×Q8C2414yes—
583C22×D4C2412yes—
584C22×D4C2411yescharacteristic
585C23×C4C2414yes—
586C23×C4C2412yes—
587C23×C4C2412yes—
588C23×C4C2412yes—
589C23×C4C2414yes—
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C4⋊Q8—28no—
598C4⋊Q8—28no—
599C4⋊Q8—28no—
600C4⋊Q8—24no—
601C4⋊Q8—28no—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—44no—
605C4⋊Q8—44no—
606C4⋊Q8—44no—
607C4⋊Q8#4118yes—
608#126—28no—
609#126—416no—
610#125—216no—
611#125—24no—
612#125—48no—
613#125—48no—
614#125—416no—
615#124—24no—
616#123—28no—
617#123—416no—
618C22⋊Q8—216no—
619C22⋊Q8—24no—
620C22⋊Q8—216no—
621C22⋊Q8—216no—
622C22⋊Q8—48no—
623C22⋊Q8—48no—
624C22⋊Q8—48no—
625#121—24no—
626C4×Q8—216no—
627C4×Q8—216no—
628C4×Q8—28no—
629C4×Q8—28no—
630C4×Q8—28no—
631C4×Q8—28no—
632C4×Q8—216no—
633C4×Q8—216no—
634C4×Q8—24no—
635C4×Q8—24no—
636C4×Q8—24no—
637C4×Q8—48no—
638C4×Q8—48no—
639C4×Q8—48no—
640C4×Q8—48no—
641C4×D4—28no—
642C4×D4—28no—
643C4×D4—28no—
644C4×D4—24no—
645C4×D4—24no—
646C4×D4—24no—
647#117—216no—
648#117—28no—
649#117—44no—
650#117—48no—
651#117—416no—
652#117—48no—
653C2×C4⋊C4—28no—
654C2×C4⋊C4—216no—
655C2×C4⋊C4—28no—
656C2×C4⋊C4—28no—
657C2×C4⋊C4—28no—
658C2×C4⋊C4—28no—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2418yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C4⋊C4C2418yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2418yes—
710C2×C4⋊C4C2418yes—
711C2×C4⋊C4C2418yes—
712C2×C4⋊C4C2418yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C22⋊C4C2412yes—
717C2×C22⋊C4C2418yes—
718C2×C22⋊C4C2412yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2412yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2412yes—
724C2×C22⋊C4C2412yes—
725C2×C22⋊C4C2412yes—
726C2×C22⋊C4C2412yes—
727C2×C22⋊C4C2412yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2412yes—
731C2×C22⋊C4C2412yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C42—216no—
735C2×C42—24no—
736C2×C42—24no—
737C2×C42—24no—
738C2×C42—28no—
739C2×C42—24no—
740C2×C42—24no—
741C2×C42—42no—
742C2×C42#4118yes—
743C2×C42C2411yescharacteristic
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2418yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2412yes—
752C2×C42C2414yes—
753C2×C42C2412yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2411yescharacteristic
760C2×C42C2412yes—
761C2×C42C2411yescharacteristic
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770C2×C42C2411yescharacteristic
771C2×C42C2411yescharacteristic
772C2×C42C2411yescharacteristic
773C2×C42C2411yescharacteristic
774C2×C42C2411yescharacteristic
775C2×C42C2411yescharacteristic
776C2×C42C2418yes—
777C2×C42C2418yes—
778C2×C42C2418yes—
779C2×C42C2418yes—
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788C2×C42C2411yescharacteristic
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2412yes—
798#95C2412yes—
799#95C2412yes—
800#95C2412yes—
801#95C2412yes—
802#95C2412yes—
803#95C2412yes—
804#95C2412yes—
805#95C2418yes—
806#95C2418yes—
807#95C2418yes—
808#95C2412yes—
809#95C2412yes—
810#95C2412yes—
811#95C2412yes—
812#95C2412yes—
813#95C2412yes—
814#95C2412yes—
815#95C2412yes—
816#95C2412yes—
817#95C2418yes—
818#95C2418yes—
819#95C2412yes—
820#95C2412yes—
821#95C2412yes—
822#95C2418yes—
823#95C2418yes—
824#95C2418yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2418yes—
837C24C2512yes—
838C24C2511yescharacteristic
839C2×Q8—24no—
840C2×Q8—28no—
841C2×Q8—24no—
842C2×Q8—22no—
843C2×Q8—28no—
844C2×Q8—28no—
845C2×Q8—24no—
846C2×Q8—28no—
847C2×Q8—22no—
848C2×Q8—22no—
849C2×Q8—28no—
850C2×Q8—28no—
851C2×Q8—24no—
852C2×Q8—24no—
853C2×Q8—44no—
854C2×Q8—44no—
855C2×Q8—44no—
856C2×Q8—432no—
857C2×Q8C2×#4118yes—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—28no—
875C22×C4—28no—
876C22×C4—22no—
877C22×C4—28no—
878C22×C4—22no—
879C22×C4—28no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—28no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—44no—
895C22×C4C2×#4114yes—
896C22×C4C2×#4114yes—
897C22×C4C2×#4114yes—
898C22×C4H(5,𝔽2)14yes—
899C22×C42−1+414yes—
900C22×C4C2512yes—
901C22×C4C2511yescharacteristic
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2514yes—
905C22×C4C2512yes—
906C22×C4C2514yes—
907C22×C4C2511yescharacteristic
908C22×C4C2518yes—
909C22×C4C2518yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2512yes—
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2514yes—
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2511yescharacteristic
924C22×C4C2511yescharacteristic
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—28no—
941C4⋊C4—22no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—216no—
945C4⋊C4—216no—
946C4⋊C4—28no—
947C4⋊C4—24no—
948C4⋊C4—24no—
949C4⋊C4—24no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—24no—
953C4⋊C4—216no—
954C4⋊C4—28no—
955C4⋊C4—24no—
956C4⋊C4—24no—
957C4⋊C4—24no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—28no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—44no—
974C4⋊C4—44no—
975C4⋊C4—48no—
976C4⋊C4—48no—
977C4⋊C4—44no—
978C4⋊C4—48no—
979C4⋊C4—48no—
980C4⋊C4—48no—
981C4⋊C4—44no—
982C4⋊C4C2×#4118yes—
983C4⋊C4C2×#4118yes—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—216no—
987C22⋊C4—24no—
988C22⋊C4—24no—
989C22⋊C4—216no—
990C22⋊C4—24no—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—24no—
994C22⋊C4—24no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—48no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C42—28no—
1003C42—28no—
1004C42—24no—
1005C42—24no—
1006C42—28no—
1007C42—28no—
1008C42—24no—
1009C42—22no—
1010C42—22no—
1011C42—22no—
1012C42—24no—
1013C42—216no—
1014C42—22no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—24no—
1019C42—22no—
1020C42—22no—
1021C42—22no—
1022C42—22no—
1023C42—22no—
1024C42—22no—
1025C42—22no—
1026C42—22no—
1027C42—22no—
1028C42—22no—
1029C42—24no—
1030C42—24no—
1031C42—24no—
1032C42—22no—
1033C42—22no—
1034C42—24no—
1035C42—41no—
1036C42—41no—
1037C42—48no—
1038C42—48no—
1039C42—48no—
1040C42—48no—
1041C42C2×#4114yes—
1042C42C2×#4114yes—
1043C42C2×#4114yes—
1044C42C2×#4114yes—
1045C42C2×#4114yes—
1046C422−1+414yes—
1047C422−1+414yes—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23C22×#4112yes—
1060C23C2×H(5,𝔽2)12yes—
1061C23C2×2−1+412yes—
1062C23C2611yescharacteristic
1063Q8—216no—
1064Q8—416no—
1065Q8—48no—
1066Q8—44no—
1067Q8—416no—
1068Q8—88no—
1069D4—48no—
1070D4—44no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—24no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—24no—
1088C2×C4—21no—
1089C2×C4—28no—
1090C2×C4—28no—
1091C2×C4—28no—
1092C2×C4—28no—
1093C2×C4—28no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—28no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—28no—
1111C2×C4—28no—
1112C2×C4—24no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—28no—
1128C2×C4—28no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—28no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—44no—
1137C2×C4—44no—
1138C2×C4—416no—
1139C2×C4—416no—
1140C2×C4—48no—
1141C2×C4—48no—
1142C2×C4—48no—
1143C2×C4C22×#4112yes—
1144C2×C4C22×#4118yes—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4112yes—
1147C2×C4C22×#4112yes—
1148C2×C4C22×#4112yes—
1149C2×C4C22×#4112yes—
1150C2×C4C22×#4112yes—
1151C2×C4C22×#4112yes—
1152C2×C4C22×#4112yes—
1153C2×C4C2×H(5,𝔽2)12yes—
1154C2×C4C2×H(5,𝔽2)12yes—
1155C2×C4C2×2−1+412yes—
1156C2×C4C2×2−1+412yes—
1157C2×C4C2×2−1+412yes—
1158C2×C4C2×2−1+412yes—
1159C2×C4C2×2−1+412yes—
1160C2×C4C2×2−1+412yes—
1161C2×C4C2×2−1+412yes—
1162C2×C4C2×2−1+412yes—
1163C2×C4#58512yes—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22#351114yes—
1178C22C23×#4111yescharacteristic
1179C22C23×#4111yescharacteristic
1180C22C22×H(5,𝔽2)11yescharacteristic
1181C22C22×2−1+411yescharacteristic
1182C22C22×2−1+411yescharacteristic
1183C22C22×2−1+411yescharacteristic
1184C22C2×#58511yescharacteristic
1185C4—22no—
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—22no—
1190C4—22no—
1191C4—22no—
1192C4—22no—
1193C4—28no—
1194C4—42no—
1195C4—48no—
1196C4—42no—
1197C4—44no—
1198C4—44no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—41no—
1203C4—48no—
1204C4—42no—
1205C4—41no—
1206C4—42no—
1207C4—44no—
1208C4#347514yes—
1209C4#350914yes—
1210C4#352214yes—
1211C4#352314yes—
1212C2—24no—
1213C2—82no—
1214C2C2×#347511yescharacteristic
1215C2C2×#352211yescharacteristic
1216C2C2×#352311yescharacteristic
1217C2C2×#351111yescharacteristic
1218C2C2×#350911yescharacteristic
1219C2#6283511yescharacteristic
1220C2#6283711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59665C2semidirect
2. #59639C2semidirect
3. #59456C2semidirect
4. #59426C2semidirect
5. #59289C2semidirect
6. #59111C2semidirect
7. #39535C2semidirect
8. #39534C2semidirect
9. #39192C2semidirect
10. #38976C2semidirect
11. #38111C2semidirect
12. #36645C2semidirect
13. #36598C2semidirect
14. #36563C2semidirect
15. #36194C2semidirect
16. #36193C2semidirect
18. #36181C2semidirect
19. #36177C2semidirect
21. #36134C2semidirect
22. #36129C2semidirect
23. #35594C2semidirect
24. #35291C2semidirect
26. #34225C2semidirect
27. #34196C2semidirect
28. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#596652
#596392
#594562
#594262
#592892
#591112
#395352
#395342
#391922
#389762
#381112
#366452
#365982
#365632
#361942
#361932
#361862
#361812
#361772
#361762
#361342
#361292
#355942
#352912
#352472
#342252
#341962
C2×C4×C4⋊Q82
C4×#5292